Relationship between scattering matrix and spectrum of quantum graphs
Mathematical Physics
2011-10-19 v2 math.MP
Abstract
We investigate the equivalence between spectral characteristics of the Laplace operator on a metric graph, and the associated unitary scattering operator. We prove that the statistics of level spacings, and moments of observations in the eigenbases coincide in the limit that all bond lengths approach a positive constant value.
Cite
@article{arxiv.0801.4104,
title = {Relationship between scattering matrix and spectrum of quantum graphs},
author = {G. Berkolaiko and B. Winn},
journal= {arXiv preprint arXiv:0801.4104},
year = {2011}
}
Comments
19 pages, 3 figures; substituted a proof for a reference to a published one, other minor updates